Algebra Seminar: Iorgov -- Ising correlations and elliptic determinants

There will be an Algebra Seminar on Friday 21 October, given by Nikolai Iorgov.  

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Speaker: Nikolai Iorgov (Bogolyubov Institute for Theoretical Physics) 

Date: Friday 21 October 

Time: 12:05-12:55pm 

Venue: Carslaw 175 

Title: 

Ising correlations and elliptic determinants 

Abstract: 

Correlation functions of the two-dimensional Ising model on the periodic lattice can be
expressed in terms of form factors - matrix elements of the spin operator in the basis
of common eigenvectors of the transfer matrix and translation operator.  Free-fermion
structure of the model implies that any multiparticle form factor is given by the
pfaffian of a matrix constructed from the two-particle ones.  Crossed two-particle form
factors can be obtained by inverting a block of the matrix of linear transformation
induced on fermions by the spin conjugation.  We show that the corresponding matrix is
of elliptic Cauchy type and use this observation to solve the inversion problem
explicitly.  Non-crossed two-particle form factors are then obtained using theta
functional interpolation formulas.  This gives a new simple proof of the factorized
formulas for periodic Ising form factors, conjectured by A.  Bugrij and O.  Lisovyy.
(The talk is based on arXiv:1012.2856).  

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